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Nonparametric check for partial linear errors-in-covariables models with validation data

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  • Wangli Xu
  • Lixing Zhu

Abstract

In this paper, we investigate the goodness-of-fit test of partial linear regression models when the true variable in the linear part is not observable but the surrogate variable $$\tilde{X}$$ X ~ , the variable in the non-linear part $$T$$ T and the response $$Y$$ Y are exactly measured. In addition, an independent validation data set for $$X$$ X is available. By a transformation, it is found that we only need to check whether the linear model is plausible or not. We estimate the conditional expectation of $$X$$ X under a given the surrogate variable with the help of the validation sample. Finally, a residual-based empirical test for the partial linear models is constructed. A nonparametric Monte Carlo test procedure is used, and the null distribution can be well approximated even when data are from alternative models converging to the hypothetical model. Simulation results show that the proposed method works well. Copyright The Institute of Statistical Mathematics, Tokyo 2015

Suggested Citation

  • Wangli Xu & Lixing Zhu, 2015. "Nonparametric check for partial linear errors-in-covariables models with validation data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(4), pages 793-815, August.
    • Handle: RePEc:spr:aistmt:v:67:y:2015:i:4:p:793-815
    DOI: 10.1007/s10463-014-0476-7
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    References listed on IDEAS

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    1. Wangli Xu & Xu Guo, 2013. "Checking the adequacy of partial linear models with missing covariates at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 473-490, June.
    2. W. Stute & W. L. Xu & L. X. Zhu, 2008. "Model diagnosis for parametric regression in high-dimensional spaces," Biometrika, Biometrika Trust, vol. 95(2), pages 451-467.
    3. Wangli Xu & Xu Guo & Lixing Zhu, 2012. "Goodness-of-fitting for partial linear model with missing response at random," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 103-118.
    4. Qi-Hua Wang, 2003. "Estimation of partial linear error-in-response models with validation data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(1), pages 21-39, March.
    5. Wang, Qihua, 1999. "Estimation of Partial Linear Error-in-Variables Models with Validation Data," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 30-64, April.
    6. Stute, Winfried & Xue, Liugen & Zhu, Lixing, 2007. "Empirical Likelihood Inference in Nonlinear Errors-in-Covariables Models With Validation Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 332-346, March.
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    Cited by:

    1. Zhihua Sun & Dongshan Luo & Xiaohua Zhou & Qingzhao Zhang, 2021. "Comparative studies on the adequacy check of parametric measurement error models with auxiliary variable," Statistical Papers, Springer, vol. 62(4), pages 1723-1751, August.
    2. Otsu, Taisuke & Taylor, Luke, 2021. "Specification Testing For Errors-In-Variables Models," Econometric Theory, Cambridge University Press, vol. 37(4), pages 747-768, August.
    3. Sun, Zhihua & Chen, Feifei & Zhou, Xiaohua & Zhang, Qingzhao, 2017. "Improved model checking methods for parametric models with responses missing at random," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 147-161.

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